"Richie addressed it yesterday, it's all speculation," he said.
"(Barrett's wife) Hannah and I haven't spoken to any media, you're the first I've spoken to about this.
"We don't have much in front of us, in facts and details. It's hard to make a decision.
"As professional rugby players we're required to turn up and perform – it's not every day you get to pull on the black jersey. It's not something you take lightly, that decision.
"This thing is changing every day, it is not even confirmed that South Africa and Argentina will come over. There's a lot of water to go under the bridge."
Barrett said he was excited about the prospect of playing in the afternoon Bledisloe Cup games in New Zealand.
"A big tick all round," said Barrett.
The initial media report suggested that TJ Perenara and Sevu Reece could also be in doubt.
The partners of Mo'unga and Perenara have recently given birth while Reece – like Barrett – is an expectant father.
Mo'unga described the report as "laughable".
"When speculation comes out like that it can be harmful and sad for family members during these uncertain times," he said.
"I'm sure players with newborn babies, soon-to-be-fathers will have conversations and make those decisions in their own time with (All Blacks) coach Ian Foster and the management."
The report said some All Blacks told New Zealand Rugby they don't want to leave their families for up to 10 weeks for the Rugby Championship in Australia, which could include spending Christmas in quarantine.
Foster said discussions were being held with players and NZR was "trying to be responsible employers".
